Here are the official answers
So the question here is:
1) In a game we played last weekend, one player had taken the "Banker" as a hostage, but did not get hold of any Strongbox during the course of the game. However, the End of Game event was "Sharing the loot", and of course our cunning bandit managed to finish the game in a space with another bandit who actually had a strongbox in his possession, giving them both $500 from that strongbox.
Would the bandit with the "Banker" now be able to claim the $1000 ransom from the hostage card? In other words: is his/her share of a Strongbox enough to trigger the ransom condition of the Hostage card?
Nope. The bandit with the Banker does not get the $1000 ransom if he does not have the Strongbox token in his possession, even if he shares the strongbox of another player thanks to the card "Sharing loot".
And as a follow-up question, what if the situation were vice versa:
2) The bandit has the Banker as a Hostage and this time, is in possession of one Strongbox. However, "Sharing the loot" is the End of Game event again and another bandit is in his/her space. Effectively, only half of a Strongbox is owned now, right? Would that still be enough to trigger the Banker's ransom condition?
In that case, the bandit with the Banker is in possession of one strongbox. Thus he gets the ransom even if he has to share this strongbox with other players.
I guess it all boils down to:
3) Does the ransom triggering condition "...have at least one strongbox" check if
a) ... the bandit physically has at least one Strongbox token in possession at the end of the game (regardless of whether it needs to be shared with other bandits or not?) OR
Yes, it triggers the ransom condition.
b) ... the value of the acquired Strongbox loot is at least $1000 at the end of the game (regardless of whether the bandit acquired it him-/herself or other bandits did?) OR
The value of the money remaining from the strongbox at the end of the game does not count.
c) ... the bandit has gotten hold of / has access to any piece/share of Strongbox loot at all at the end of the game?
What matters is that the player has a Strongbox token in front of him at the end of the game. This is not valid if he shares the strongbox of someone else.